If their public statements are any indication, President Donald Trump and his secretary of Defense are quietly at odds with each other over several crucial national security policies, including how to deal with Russia.

Throughout his tenure in the Trump administration, Defense Secretary James Mattis, a revered Marine with a military career spanning four decades, has either downplayed or appeared out of step with the president's swift policy directives.

For instance, Mattis appeared to be a non-entity in Trump's highly anticipated meeting with Russian President Vladimir Putin unlike Secretary of State Mike Pompeo and national security advisor John Bolton. The Pentagon chief said he spoke with White House chief of staff John Kelly and Bolton after Trump concluded his trip to Helsinki – but he didn't say anything about whether he spoke with the president.

"I have talked immediately after the Helsinki summit, both the chief of staff and the national security advisor called me, I wouldn't say immediately but as soon as they got free," Mattis told reporters Friday.

Dana White, Secretary Mattis' assistant for public affairs, responded to CNBC's request for comment on the matter:

"Secretary Mattis is the principal advisor to the president on matters of national defense. The secretary routinely consults and advises the president, fellow cabinet members, and the National Security Council on a variety of topics, to include implementing the president's National Security Strategy. The secretary's priorities are aligned with the administration. He remains focused on building a more lethal force, strengthening our alliances and reforming the way we do business."

The White House did not immediately respond to CNBC's request for comment.

Yet while the Defense secretary has denied that the Pentagon's stances are inconsistent with the White House's, there are several key issues where evidence points to the contrary. Here's a roundup of subjects where Mattis and Trump have shown some stark policy differences.

The U.S. and Russia working together in war-torn Syria

President Donald Trump and Russian President Vladimir Putin shake hands as they hold a joint news conference after their meeting in Helsinki, Finland July 16, 2018.

Grigory Dukor | Reuters

Background: The last time the Trump administration crossed paths with Russia in Syria was in April, when the U.S. and its allies conducted precision missile strikes against the Assad regime. The strikes were in retaliation for a chemical attack carried out by Assad-supporters on Syrian civilians.

In a speech from the White House, Trump directly called out Russia and Iran, which back the regime of Assad.

"To Iran and to Russia, I ask: What kind of a nation wants to be associated with the mass murder of innocent men, women and children?" Trump said. "Hopefully someday we will get along with Russia, and maybe even Iran. But maybe not."

The brutal conflict in Syria has largely been defined by foreign interventions. Russia, Iran and Turkey are the three major powers influencing war-torn Syria.

What Trump said:During a joint news conference with Putin in Helsinki, Trump recommended that the U.S. and Russian military work together on the ground in Syria.

"As we discussed at length, the crisis in Syria is a complex one. Cooperation between our two countries [U.S. and Russia] has the potential to save hundreds of thousands of lives [in Syria]," Trump.

What Mattis said: Last week, Mattis told reporters that there were "no policy changes " to come out of Trump's meeting with Putin in Helsinki.

When asked whether the president had asked him to start working with Russia on the ground in Syria, Mattis said: "No, my job is to destroy ISIS and to make certain we put in place a local security force, train them up so ISIS can't get back in."

Mattis did add, however, that he was in favor of the U.S. holding discussions with countries that America has big disagreements with. "I mean that's how you repair those disagreements," he said.

Trump's call for Russia to join the G-7

L-R: British Prime Minister Theresa May, German Chancellor Angela Merkel, U.S. President Donald Trump, Canada's Prime Minister Justin Trudeau, French President Emmanuel Macron, Japanese Prime Minister Shinzo Abe and Italian Prime Minister Giuseppe Conte pose for a family photo at the G7 Summit in the Charlevoix city of La Malbaie, Quebec, Canada, June 8, 2018.

Leah Millis | Reuters

Background: Russia's 2014 annexation of Crimea resulted in rounds of international sanctions and Moscow's dismissal from the G-8. In recent weeks, Trump has left the door open for a reversal by saying "we'll see what happens."

An about-face on Ukraine's Crimean peninsula would completely upend U.S. foreign policy and its stated commitment to ally Ukraine. At the G-7 meeting in June, Trump shocked leaders by arguing that the annexed Crimean peninsula should belong to Russia and Moscow should rejoin the global group.

"I think it would be an asset to have Russia back in," Trump said at the G-7 summit. "I think it would be good for the world. I think it would be good for Russia. I think it would be good the United States. I think it would be good for all of the countries of the current G-7. I think the G-8 would be better."

What Mattis said: A week later, Mattis tore into Putin for its annexation of the Crimean peninsula and its invasion of Georgia.

"For the first time since World War II, Russia has been the nation that has redrawn international borders by force of arms in Georgia and Ukraine, while pursuing veto authority over their neighbors' diplomatic, economic and security decisions," Mattis said during his remarks in June at the U.S. Naval War College graduation.

"His actions are designed not to challenge our arms, but to undercut and compromise our belief in our ideals," he added, referring to Putin.

The Pentagon chief also singled out the Russian president for undermining one of America's most powerful military alliances.

"Putin seeks to shatter NATO," Mattis said. "He aims to diminish the appeal of the Western democratic model and attempts to undermine America's moral authority."

Trump's threat to Turkey and the U.S. citizen hanging in limbo

American Pastor Andrew Craig Brunson (C), who was charged with committing crimes, including spying for the PKK terror group and the Fetullah Terrorist Organization, in Izmir, Turkey on July 25, 2018.

Evren Atalay | Anadolu Agency | Getty Images

Background: In October 2016, Turkey detained American pastor Andrew Brunson because he was accused of spying and attempting to overthrow the government. Brunson has denied all charges.

Relations between the U.S. and Turkey have become tense over the trial of Brunson despite Ankara's recent move to transfer the American citizen to house arrest. Last week, Trump threatened to impose sanctions on Turkey, which prompted an angry response from Ankara and further escalating tensions between the two NATO allies.

What Trump said: In a July 26 tweet Trump threatened to slap "large sanctions" on Turkey unless it freed a U.S. citizen which Ankara is currently detaining.

"The United States will impose large sanctions on Turkey for their long time detainment of Pastor Andrew Brunson, a great Christian, family man and wonderful human being," Trump wrote in a tweet. "He is suffering greatly. This innocent man of faith should be released immediately!"

The controversy rages as Congress is inching closer to blocking the transfer of two F-35 jets to NATO ally Turkey.

What Mattis said: When asked about Trump's recent tweets regarding Turkey, Mattis downplayed the threats. "No impact on U.S.-Turkey relations, military operations at this time," Mattis said. "We continue to work very closely together."

Mattis did not elaborate on the potential blockade of the F-35 jets to Turkey. "No effect," Mattis said flatly on the F-35 matter. "As I was saying, we've had no problem."

Trump's cancellation of a joint exercise with South Korea

Department of Defense photo

Background: For the past 14 years, the U.S. Air Force's B-1B Lancer, B-52 Stratofortress and B-2 Spirit bombers have continuously rotated through Guam in an effort to show American commitment to allies in the region, namely Japan and South Korea.

Similarly, the U.S. conducts bilateral military exercises with its counterparts in South Korea despite opposition from North Korean leader Kim Jong Un.

The reclusive leader from the North consistently calls the military drills between the U.S. and South Korea a "provocation" and a test run for a future invasion. Shortly after Trump met with Kim in Singapore, the president cancelled the U.S. military's Freedom Guardian joint exercise with South Korea.

What Trump said: Trump described the Pentagon's exercises with South Korea as being "inappropriate" and referred to them as "war games." He also cited cost savings.

"No. 1, we save money. A lot. And No. 2, it really is something that I think they [North Korea] very much appreciated," Trump said in the wake of the Singapore summit.

Trump also said that flying U.S. Air Force bombers in regional training missions is another drain on resources.

According to estimates that the U.S. Air Force provided, the B-2 has an operational flight cost of $130,000 an hour and the B-1B operates at $95,000 an hour.

Pentagon spokesman U.S. Army Col. Rob Manning described Freedom Guardian as a "keystone exercise" that is designed to "enhance the readiness" of forces on the Korean Peninsula.

More than a week after Trump's announcement to call off the drills, the Pentagon made good on the president's promise and "indefinitely suspended" them.

Mattis defended the cancellation of the drills with South Korea saying it "increased opportunity for our diplomats to negotiate, increasing prospects for a peaceful solution on the Korean Peninsula." However, according to an NBC News report, Mattis was not expecting Trump's announcement that the exercises would be canceled.

Instead, Mattis found out from one of his assistant secretaries the morning after the summit had concluded, according to a former senior White House official.